A preliminary study has shown that 3-oxy-pyrylium is capable of cycloadditions to form seven-, eight-, and ten-membered carbocyclic rings. This constitutes a powerful new tool for organic synthesis and we propose to explore its scope and applicability. In particular it makes possible unusually short syntheses of two large classes of sesquiterpenes, the pseudoguaianolides (7-rings) and the germacranolides (10-rings). Hundreds of examples have been isolated from nature in the search for cytotoxic agent and a number have been found active. These short syntheses can make them available in quantity for further testing, as well as afford routes to chemical derivatives. The variety in the natural pseudoguaianolides stems from all variations in stereochemistry at three of the six chiral centers on the seven-membered ring, and the synthetic routes available from the cycloadducts can create all these variants in short, parallel routes with strict stereo control, much shorter than any presently in the literature. The same brevity characterizes the syntheses of the cytotoxic germacranolides. A short synthesis is also proposed for periplanone B, the sex attractant of the American cockroach, using the same ten-membered ring cycloadduct.